Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the di...Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.展开更多
A great challenge faced by wireless sensor networks(WSNs) is to reduce energy consumption of sensor nodes. Fortunately, the data gathering via random sensing can save energy of sensor nodes. Nevertheless, its randomne...A great challenge faced by wireless sensor networks(WSNs) is to reduce energy consumption of sensor nodes. Fortunately, the data gathering via random sensing can save energy of sensor nodes. Nevertheless, its randomness and density usually result in difficult implementations, high computation complexity and large storage spaces in practical settings. So the deterministic sparse sensing matrices are desired in some situations. However,it is difficult to guarantee the performance of deterministic sensing matrix by the acknowledged metrics. In this paper, we construct a class of deterministic sparse sensing matrices with statistical versions of restricted isometry property(St RIP) via regular low density parity check(RLDPC) matrices. The key idea of our construction is to achieve small mutual coherence of the matrices by confining the column weights of RLDPC matrices such that St RIP is satisfied. Besides, we prove that the constructed sensing matrices have the same scale of measurement numbers as the dense measurements. We also propose a data gathering method based on RLDPC matrix. Experimental results verify that the constructed sensing matrices have better reconstruction performance, compared to the Gaussian, Bernoulli, and CSLDPC matrices. And we also verify that the data gathering via RLDPC matrix can reduce energy consumption of WSNs.展开更多
This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information ...This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.展开更多
Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtaine...Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional (RRF) criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming (QCQP) problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-A...Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.展开更多
In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a...In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.展开更多
为有效抑制椒盐噪声对图像信息的影响,根据椒盐噪声随机破坏图像中像素值的显著特征,本文提出一种耦合噪声检测的自适应模糊正则化噪声去除模型。一方面,基于L_(1)范数建立数据保真项,实现对图像统计分布进行有效拟合。另一方面,通过对...为有效抑制椒盐噪声对图像信息的影响,根据椒盐噪声随机破坏图像中像素值的显著特征,本文提出一种耦合噪声检测的自适应模糊正则化噪声去除模型。一方面,基于L_(1)范数建立数据保真项,实现对图像统计分布进行有效拟合。另一方面,通过对图像中像素相似性的有效量化实现图像中噪声的检测,并将此耦合至正则项中,使得模型可依据像素点实际受噪声的污染对其施加惩罚程度,最终实现椒盐噪声的自适应模糊去除。本文采用交替方向乘子法(Alternating direction method of multipliers,ADMM)进行模型的数值结果实现,并运用峰值信噪比(Peak signal-to-noise ratio,PSNR)及结构相似性(Structural similarity,SSIM)对实验结果进行评定。实验结果表明,本文提出的模型在PSNR及SSIM方面得到显著提升,其中对于灰度图像的去噪实验PSNR最高可提高1.3dB,SSIM最高可提高0.2。展开更多
Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matri...Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.展开更多
Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases wi...Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.展开更多
It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obt...It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.展开更多
Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has ap...Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image processing, text mining, recommendation systems and a variety of other fields. Since its inception, the NMF algorithm has been modified and explored by numerous authors. One such modification involves the addition of auxiliary constraints to the objective function of the factorization. The purpose of these auxiliary constraints is to impose task-specific penalties or restrictions on the objective function. Though many auxiliary constraints have been studied, none have made use of data-dependent penalties. In this paper, we propose Zellner nonnegative matrix factorization (ZNMF), which uses data-dependent auxiliary constraints. We assess the facial recognition performance of the ZNMF algorithm and several other well-known constrained NMF algorithms using the Cambridge ORL database.展开更多
基金supported by the National Natural Science Foundation of China(No.51877013),(ZJ),(http://www.nsfc.gov.cn/)the Natural Science Foundation of Jiangsu Province(No.BK20181463),(ZJ),(http://kxjst.jiangsu.gov.cn/)sponsored by Qing Lan Project of Jiangsu Province(no specific grant number),(ZJ),(http://jyt.jiangsu.gov.cn/).
文摘Currently,functional connectomes constructed from neuroimaging data have emerged as a powerful tool in identifying brain disorders.If one brain disease just manifests as some cognitive dysfunction,it means that the disease may affect some local connectivity in the brain functional network.That is,there are functional abnormalities in the sub-network.Therefore,it is crucial to accurately identify them in pathological diagnosis.To solve these problems,we proposed a sub-network extraction method based on graph regularization nonnegative matrix factorization(GNMF).The dynamic functional networks of normal subjects and early mild cognitive impairment(eMCI)subjects were vectorized and the functional connection vectors(FCV)were assembled to aggregation matrices.Then GNMF was applied to factorize the aggregation matrix to get the base matrix,in which the column vectors were restored to a common sub-network and a distinctive sub-network,and visualization and statistical analysis were conducted on the two sub-networks,respectively.Experimental results demonstrated that,compared with other matrix factorization methods,the proposed method can more obviously reflect the similarity between the common subnetwork of eMCI subjects and normal subjects,as well as the difference between the distinctive sub-network of eMCI subjects and normal subjects,Therefore,the high-dimensional features in brain functional networks can be best represented locally in the lowdimensional space,which provides a new idea for studying brain functional connectomes.
基金supported by the National Natural Science Foundation of China(61307121)ABRP of Datong(2017127)the Ph.D.’s Initiated Research Projects of Datong University(2013-B-17,2015-B-05)
文摘A great challenge faced by wireless sensor networks(WSNs) is to reduce energy consumption of sensor nodes. Fortunately, the data gathering via random sensing can save energy of sensor nodes. Nevertheless, its randomness and density usually result in difficult implementations, high computation complexity and large storage spaces in practical settings. So the deterministic sparse sensing matrices are desired in some situations. However,it is difficult to guarantee the performance of deterministic sensing matrix by the acknowledged metrics. In this paper, we construct a class of deterministic sparse sensing matrices with statistical versions of restricted isometry property(St RIP) via regular low density parity check(RLDPC) matrices. The key idea of our construction is to achieve small mutual coherence of the matrices by confining the column weights of RLDPC matrices such that St RIP is satisfied. Besides, we prove that the constructed sensing matrices have the same scale of measurement numbers as the dense measurements. We also propose a data gathering method based on RLDPC matrix. Experimental results verify that the constructed sensing matrices have better reconstruction performance, compared to the Gaussian, Bernoulli, and CSLDPC matrices. And we also verify that the data gathering via RLDPC matrix can reduce energy consumption of WSNs.
基金supported by the National Natural Science Foundation of China(61702251,61363049,11571011)the State Scholarship Fund of China Scholarship Council(CSC)(201708360040)+3 种基金the Natural Science Foundation of Jiangxi Province(20161BAB212033)the Natural Science Basic Research Plan in Shaanxi Province of China(2018JM6030)the Doctor Scientific Research Starting Foundation of Northwest University(338050050)Youth Academic Talent Support Program of Northwest University
文摘This paper proposes a Graph regularized Lpsmooth non-negative matrix factorization(GSNMF) method by incorporating graph regularization and L_p smoothing constraint, which considers the intrinsic geometric information of a data set and produces smooth and stable solutions. The main contributions are as follows: first, graph regularization is added into NMF to discover the hidden semantics and simultaneously respect the intrinsic geometric structure information of a data set. Second,the Lpsmoothing constraint is incorporated into NMF to combine the merits of isotropic(L_2-norm) and anisotropic(L_1-norm)diffusion smoothing, and produces a smooth and more accurate solution to the optimization problem. Finally, the update rules and proof of convergence of GSNMF are given. Experiments on several data sets show that the proposed method outperforms related state-of-the-art methods.
基金Supported by National Natural Science Foundation of China
文摘Let A=M-N be a regular splitting of an M-matrix. We study the spectral properties of the ineration matrix M-1N. Under a mild assumption on M-1 N. some necessary and sufficent conditions such that p(M-1N)=1 are obtained and the algebraic multiplicity and the index associated with eigenvalue 1 in M-1N are considered.
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional (RRF) criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming (QCQP) problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
文摘Based on the topological analysis of three-phase matrix AC to AC conversion circuit, an AC to AC nine-switch matrix isequivalent to rectification part and conversion part. The Matrix converter can be viewed as AC-DC-AC converter, the asymmetricregular sampling method SPWM(Sine Pulse Width Modulation) is studied and applied in the three-phase matrix AC to AC converter,Based on Matlab/simulink the simulation of the matrix converter with such strategy is carried out. Inductive load simulation is carriedout on the matrix converter prototype. The simulation results verify the workability of the asymmetric regular sampling method SPWMstrategy for matrix converter.
文摘In this paper we introduce the sign matrix of a nonlinear system of equations x = Gx to characterize its hybrid and asynchronous monotonicity as well as convexity. Based on the configuration of the matrix, we define a new type of regular splittings of the system with which the solvability and construction of solutions for the system are transformed to those of the couple systems of the splitting formIt is shown that this couple systems is a general model for developing monotonic enclosure methods of solutions for various types of nonlinear system of equations.
文摘为有效抑制椒盐噪声对图像信息的影响,根据椒盐噪声随机破坏图像中像素值的显著特征,本文提出一种耦合噪声检测的自适应模糊正则化噪声去除模型。一方面,基于L_(1)范数建立数据保真项,实现对图像统计分布进行有效拟合。另一方面,通过对图像中像素相似性的有效量化实现图像中噪声的检测,并将此耦合至正则项中,使得模型可依据像素点实际受噪声的污染对其施加惩罚程度,最终实现椒盐噪声的自适应模糊去除。本文采用交替方向乘子法(Alternating direction method of multipliers,ADMM)进行模型的数值结果实现,并运用峰值信噪比(Peak signal-to-noise ratio,PSNR)及结构相似性(Structural similarity,SSIM)对实验结果进行评定。实验结果表明,本文提出的模型在PSNR及SSIM方面得到显著提升,其中对于灰度图像的去噪实验PSNR最高可提高1.3dB,SSIM最高可提高0.2。
基金Supported by the Natural Science Foundation of China(10071078)Supported by the Natural Science Foundation of Shandong Province(Q99A08)
文摘Let Ω be a finite dimensional central algebra and chart Ω≠2 .The matrix equation AXB-CXD=E over Ω is considered.Necessary and sufficient conditions for the existence of centro(skew)symmetric solutions of the matrix equation are given.As a particular case ,the matrix equation X-AXB=C over Ω is also considered.
文摘Constant solutions to Yang-Baxter equation are investigated over Grassmann algebra for the case of 6-vertex R-matrix. The general classification of all possible solutions over Grassmann algebra and particular cases with 2,3,4 generators are studied. As distinct from the standard case, when R-matrix over number field can have a maximum 5 nonvanishing elements, we obtain over Grassmann algebra a set of new full 6-vertex solutions. The solutions leading to regular R-matrices which appear in weak Hopf algebras are considered.
文摘It is well known that the matrix equations play a significant role in engineering and applicable sciences. In this research article, a new modification of the homotopy perturbation method (HPM) will be proposed to obtain the approximated solution of the matrix equation in the form AX = B. Moreover, the conditions are deduced to check the convergence of the homotopy series. Numerical implementations are adapted to illustrate the properties of the modified method.
文摘Nonnegative matrix factorization (NMF) is a relatively new unsupervised learning algorithm that decomposes a nonnegative data matrix into a parts-based, lower dimensional, linear representation of the data. NMF has applications in image processing, text mining, recommendation systems and a variety of other fields. Since its inception, the NMF algorithm has been modified and explored by numerous authors. One such modification involves the addition of auxiliary constraints to the objective function of the factorization. The purpose of these auxiliary constraints is to impose task-specific penalties or restrictions on the objective function. Though many auxiliary constraints have been studied, none have made use of data-dependent penalties. In this paper, we propose Zellner nonnegative matrix factorization (ZNMF), which uses data-dependent auxiliary constraints. We assess the facial recognition performance of the ZNMF algorithm and several other well-known constrained NMF algorithms using the Cambridge ORL database.